Enhanced collisional growth of a protoplanet that has an atmosphere

Inaba, Satoshi; Ikoma, Masahiro

doi:10.1051/0004-6361:20031248

Cited by 140 publications

(177 citation statements)

References 22 publications

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“…Long before this size is reached, protoplanets bind the nebular gas and form atmospheres that will enhance the capture radius (Inaba & Ikoma 2003;Tanigawa & Ohtsuki 2010). According to the results of Inaba & Ikoma (2003) this will perhaps become important when oligarchs reach 0.1 M ⊕ 3 . Our expression for the impact radius and collision rates, therefore, are lower limits when protoplanets are surrounded by a thick atmosphere.…”

Section: Discussionmentioning

confidence: 99%

“…Gas drag can provide some relief since, by damping the random motions of the planetesimals, the gravitational focusing is kept large. Moreover, the capture probability of planetesimals is also significantly increased when (proto)planets are surrounded by atmospheres (Inaba & Ikoma 2003;Tanigawa & Ohtsuki 2010) -again, gas drag is the mechanism that facilitates their accretion. Still, it is unclear if these effects are sufficient to overcome the timescale problem, i.e., to grow protoplanets to ∼10 M ⊕ within the time the gas disk dissipates (∼10 6 yr); see Levison et al (2010) for a recent review.…”

Section: Introductionmentioning

confidence: 99%

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The effect of gas drag on the growth of protoplanets

Ormel¹,

Klahr

2010

A&A

590

641

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Planetary bodies form by accretion of smaller bodies. It has been suggested that a very efficient way to grow protoplanets is by accreting particles of size km (e.g., chondrules, boulders, or fragments of larger bodies) as they can be kept dynamically cold. We investigate the effects of gas drag on the impact radii and the accretion rates of these particles. As simplifying assumptions we restrict our analysis to 2D settings, a gas drag law linear in velocity, and a laminar disk characterized by a smooth (global) pressure gradient that causes particles to drift in radially. These approximations, however, enable us to cover an arbitrary large parameter space. The framework of the circularly restricted three body problem is used to numerically integrate particle trajectories and to derive their impact parameters. Three accretion modes can be distinguished: hyperbolic encounters, where the 2-body gravitational focusing enhances the impact parameter; three-body encounters, where gas drag enhances the capture probability; and settling encounters, where particles settle towards the protoplanet. An analysis of the observed behavior is presented; and we provide a recipe to analytically calculate the impact radius, which confirms the numerical findings. We apply our results to the sweepup of fragments by a protoplanet at a distance of 5 AU. Accretion of debris on small protoplanets ( < ∼ 50 km) is found to be slow, because the fragments are distributed over a rather thick layer. However, the newly found settling mechanism, which is characterized by much larger impact radii, becomes relevant for protoplanets of ∼10 3 km in size and provides a much faster channel for growth.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The effect of gas drag on the growth of protoplanets

Ormel¹,

Klahr

2010

A&A

590

641

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“…Inaba & Ikoma (2003) showed that the presence of a dense atmosphere increases the cross section of planetesimals and they derived expressions to quantify this effect. However, Ormel & Kobayashi (2012) showed that for small particles interacting in the settling regime the presence of an atmosphere does not yield an increase in the cross section.…”

Section: Presence Of An Atmospherementioning

confidence: 99%

“…First, protoplanets with masses over ∼0.1 M ⊕ (corresponding to radii of about 5000 km forρ p = 1 g cm −3 ) begin building a hydrogen-helium atmosphere which progressively enhances their cross section (Inaba & Ikoma 2003;Tanigawa & Ohtsuki 2010). When modeling this effect with the approach of Ormel & Kobayashi (2012), we find that the effect is significant at the high end of the radius range considered here, but without affecting our conclusions: the filtering efficiency remains low even for these Earth-mass protoplanets when in the settling regime, and extremely low in the hydrodynamical regime.…”

Section: Filtering By Protoplanetsmentioning

confidence: 99%

On the filtering and processing of dust by planetesimals

Guillot

Ida

Ormel

2014

A&A

141

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Context. Circumstellar disks are known to contain a significant mass in dust ranging from micron to centimeter size. Meteorites are evidence that individual grains of those sizes were collected and assembled into planetesimals in the young solar system. Aims. We assess the efficiency of dust collection of a swarm of non-drifting planetesimals with radii ranging from 1 to 10 3 km and beyond. Methods. We calculate the collision probability of dust drifting in the disk due to gas drag by planetesimal accounting for several regimes depending on the size of the planetesimal, dust, and orbital distance: the geometric, Safronov, settling, and three-body regimes. We also include a hydrodynamical regime to account for the fact that small grains tend to be carried by the gas flow around planetesimals. Results. We provide expressions for the collision probability of dust by planetesimals and for the filtering efficiency by a swarm of planetesimals. For standard turbulence conditions (i.e., a turbulence parameter α = 10 −2 ), filtering is found to be inefficient, meaning that when crossing a minimum-mass solar nebula (MMSN) belt of planetesimals extending between 0.1 AU and 35 AU most dust particles are eventually accreted by the central star rather than colliding with planetesimals. However, if the disk is weakly turbulent (α = 10 −4 ) filtering becomes efficient in two regimes: (i) when planetesimals are all smaller than about 10 km in size, in which case collisions mostly take place in the geometric regime; and (ii) when planetary embryos larger than about 1000 km in size dominate the distribution, have a scale height smaller than one tenth of the gas scale height, and dust is of millimeter size or larger in which case most collisions take place in the settling regime. These two regimes have very different properties: we find that the local filtering efficiency x filter,MMSN scales with r −7/4 (where r is the orbital distance) in the geometric regime, but with r −1/4 to r 1/4 in the settling regime. This implies that the filtering of dust by small planetesimals should occur close to the central star and with a short spread in orbital distances. On the other hand, the filtering by embryos in the settling regime is expected to be more gradual and determined by the extent of the disk of embryos. Dust particles much smaller than millimeter size tend only to be captured by the smallest planetesimals because they otherwise move on gas streamlines and their collisions take place in the hydrodynamical regime. Conclusions. Our results hint at an inside-out formation of planetesimals in the infant solar system because small planetesimals in the geometrical limit can filter dust much more efficiently close to the central star. However, even a fully-formed belt of planetesimals such as the MMSN only marginally captures inward-drifting dust and this seems to imply that dust in the protosolar disk has been filtered by planetesimals even smaller than 1 km (not included in this study) or that it has been assembled into planetesi...

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“…For the purpose of the collision rate, the capture radius of the protoplanet should depend upon the mass of the protoplanet, upon the planetesimals' velocity with respect to the protoplanet, upon the density profile of the envelope, ρ(r), and upon the size of the accreted planetesimals (smaller planetesimals are more affected by the gas drag of the envelope and therefore are easier to capture). As in Guilera et al (2010), here we adopt the prescription of Inaba & Ikoma (2003) where the capture radius R can be obtained by solving the following equation…”

Section: The Accretion Rate Of Solidsmentioning

confidence: 99%

Planet formation models: the interplay with the planetesimal disc

Fortier

Alibert

Carron

et al. 2012

A&A

125

196

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Context. According to the sequential accretion model (or core-nucleated accretion model), giant planet formation is based first on the formation of a solid core which, when massive enough, can gravitationally bind gas from the nebula to form the envelope. The most critical part of the model is the formation time of the core: to trigger the accretion of gas, the core has to grow up to several Earth masses before the gas component of the protoplanetary disc dissipates. Aims. We calculate planetary formation models including a detailed description of the dynamics of the planetesimal disc, taking into account both gas drag and excitation of forming planets. Methods. We computed the formation of planets, considering the oligarchic regime for the growth of the solid core. Embryos growing in the disc stir their neighbour planetesimals, exciting their relative velocities, which makes accretion more difficult. Here we introduce a more realistic treatment for the evolution of planetesimals' relative velocities, which directly impact on the formation timescale. For this, we computed the excitation state of planetesimals, as a result of stirring by forming planets, and gas-solid interactions. Results. We find that the formation of giant planets is favoured by the accretion of small planetesimals, as their random velocities are more easily damped by the gas drag of the nebula. Moreover, the capture radius of a protoplanet with a (tiny) envelope is also larger for small planetesimals. However, planets migrate as a result of disc-planet angular momentum exchange, with important consequences for their survival: due to the slow growth of a protoplanet in the oligarchic regime, rapid inward type I migration has important implications on intermediate-mass planets that have not yet started their runaway accretion phase of gas. Most of these planets are lost in the central star. Surviving planets have masses either below 10 M ⊕ or above several Jupiter masses. Conclusions. To form giant planets before the dissipation of the disc, small planetesimals (∼0.1 km) have to be the major contributors of the solid accretion process. However, the combination of oligarchic growth and fast inward migration leads to the absence of intermediate-mass planets. Other processes must therefore be at work to explain the population of extrasolar planets that are presently known.

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Enhanced collisional growth of a protoplanet that has an atmosphere

Cited by 140 publications

References 22 publications

The effect of gas drag on the growth of protoplanets

The effect of gas drag on the growth of protoplanets

On the filtering and processing of dust by planetesimals

Planet formation models: the interplay with the planetesimal disc

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